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The goal of this thesis was the development and application of higher-order spectroscopic techniques. In contrast to ordinary pump–probe (PP) and two-dimensional (2D) spectroscopy, higher-order coherently detected spectroscopic methods measure a polarization that has an order of nonlinearity higher than three. The key idea of the techniques in this thesis is to isolate the higher-order signals from the lower-order signals either by their excitation frequency or by their excitation intensity dependence. Due to the increased number of interactions in higher-order spectroscopy, highly excited states can be probed. For excitonic systems such as aggregates and polymers, the fifth-order signal allows one to directly measure exciton–exciton annihilation (EEA). In polymers and aggregates, the exciton transport is not connected to a change of the absorption and can therefore not be investigated with conventional third-order techniques. In contrast, EEA can be used as a probe to study exciton diffusion in these isonergetic systems. As a part of this thesis, anisotropy in fifth-order 2D spectroscopy was investigated and was used to study geometric properties in polymers. In 2D spectroscopy, the multi-quantum signals are separated from each other by their spectral position along the excitation axis. This concept can be extended systematically to higher signals. Another approach to isolate multi-quantum signals in PP spectroscopy utilizes the excitation intensity. The PP signal is measured at specific excitation intensities and linear combinations of these measurements result in different signal contributions. However, these signals do not correspond to clean nonlinear signals because the higher-order signals contaminate the lower-order multi-quantum signals. In this thesis, a correction protocol was derived that uses the isolated multiquantum signals, both from 2D spectroscopy and from PP spectroscopy, to remove the contamination of higher-order signals resulting in clean nonlinear signals. Using the correction on the third-order signal allows one to obtain annihilation-free signals at high excitation intensities, i.e., with high signal-to-noise ratio. Isolation and correction in PP and 2D spectroscopy were directly compared by measuring the clean third-order signals of squaraine oligomers at high excitation intensities. Furthermore, higher-order PP spectroscopy was used to isolate up to the 13th nonlinear order of squaraine polymers. The demonstrated spectroscopic techniques represent general procedures to isolate clean signals in terms of perturbation theory. The technique of higher-order PP spectroscopy needs only small modifications of ordinary PP setups which opens the field of higher-order spectroscopy to the broad scientific community. The technique to obtain clean nonlinear signals allows one to systematically increase the number of interacting (quasi)particles in a system and to characterize their interaction energies and dynamics. / Das Ziel dieser Arbeit war die Entwicklung and Anwendung von spektroskopischen Techniken höherer Ordnung. Im Gegensatz zu herkömmlicher Anrege-Abfrage- und zweidimensionalen (2D) Spektroskopie, wird in kohärenzdetektierten spektroskopischen Methoden höherer Ordnung eine Polarisation gemessen, die höher als drei ist. Die Schlüsselidee der Techniken dieser Arbeit ist die Trennung Signale höherer Ordnung von den Signalen niedrigerer Ordnung, entweder durch ihre Anregungsfrequenz oder durch ihre Abhängigkeit zur Anregungsintensität. Durch die erhöhte Anzahl an Interaktionen in der Spektroskopie höherer Ordnung können auch hoch angeregte Zustände untersucht werden. Für exzitonische Systeme wie Aggregate und Polymere erlaubt das Signal fünfter Ordnung die direkte Messung der Exziton-Exziton-Annihilierung (EEA). In Polymeren und Aggregaten ist der Exziton-Transport nicht mit einer Änderung des Absoprtionsspektrums verbunden und kann daher nicht mit konventionellen Techniken dritter Ordnung untersucht werden. Im Gegensatz dazu kann EEA, die mit Spektroskopie fünfter Ordnung gemessen wird, als Sonde verwendet werden, um Exziton-Diffusion zu untersuchen. Als ein Teil dieser Arbeit wurde die Anisotropie in der 2D-Spektroskopie fünfter Ordnung untersucht, und es wurde gezeigt, dass diese geometrische Eigenschaften von Polymeren bestimmen kann. In der 2D-Spektroskopie werden die sogenannten Multiquantensignale durch ihre Position entlang der Anregungsachse von anderen Signalen getrennt. Dieses Konzept kann systematisch zu höheren Signalen erweitert werden, die durch ihre spezifische Anregungsfrequenz in dem 2D-Spektrum isoliert werden. Ein anderer Ansatz, um Multiquantensignale in der Anrege-Abfrage-Spektroskopie zu isolieren, nutzt die Anregungsintensität. Das Anrege-Abfrage-Signal wird bei spezifischen Anregungsintensitäten gemessen und Linearkombinationen dieser Messungen resultieren in verschiedenen Signalbeiträgen. Allerdings entsprechen diese Signale nicht reinen nichtlinearen Signalen, weil die Signale höherer Ordnung die Multiquantensignale niedriger Ordnung kontaminieren. In dieser Arbeit wurde ein Korrekturprotokoll entwickelt, das die isolierten Multiquantensignale sowohl in der 2D- als auch in Anrege-Abfrage-Spektroskopie nutzt, um die Kontamination durch Signale höherer Ordnung zu entfernen. Die Anwendung dieser Korrektur auf das Signal dritter Ordnung erlaubt es, annihilierungsfreie Signale bei hoher Anregungsintensität, d.h. mit hohem Signal-zu-Rausch-Verhältnis zu erhalten. Isolation und Korrektur in Anrege-Abfrage- und 2D-Spektroskopie wurden direkt miteinander verglichen, indem das kontaminierungsfreie Signal dritter Ordnung von Squarain-Oligomeren bei hoher Anregungsintensität gemessen wurde. Des Weiteren wurde Anrege-Abfrage-Spektroskopie höherer Ordnung eingesetzt, um nichtlineare Signale bis zur 13ten Ordnung in Squarain-Polymeren zu isolieren. Die gezeigten spektroskopischen Techniken stellen allgemeine Verfahren zur Isolierung verschiedener Signale im Sinne der Störungstheorie dar. Die Technik der Anrege-Abfrage-Spektroskopie höherer Ordnung erfordert nur geringfügige Änderungen an gewöhnlichen Anrege-Abfrage-Experimenten und erlaubt es, die Spektroskopie höherer Ordnung in vielen weiteren wissenschaftlichen Gebieten anzuwenden. Der Ansatz kontaminierungsfreier nichtlinearer Signale gibt die Möglichkeit, die Anzahl der wechselwirkenden Teilchen systematisch zu erhöhen und ihre Wechselwirkungsenergien und Dynamiken zu messen.

This thesis describes novel concepts for the measurement of the static and dynamic properties of the electronic structure of molecules and nanocrystals in the liquid phase by means of coherent fluorescence-detected spectroscopy in two and three frequency dimensions. These concepts are based on the systematic variation ("phase cycling") of a sequence of multiple time-delayed femtosecond excitation pulses in order to decode a multitude of novel nonlinear signals from the resulting phase-dependent fluorescence signal. These signals represent any permutation of correlations between zero-, one-, two-, and three-quantum coherences. To this end, two new phase-cycling schemes have been developed which can simultaneously resolve and discriminate several nonlinear signals of sixth order, including those of the fourth order of nonlinearity. By means of the sixth-order signals recorded in this work, static properties of highly excited electronic states in molecules such as their energies, transition dipole moments, and relative displacement of electronic potential surfaces, as well as dynamic properties in terms of their relaxation kinetics, can be ascertained. Furthermore, it was shown that these signals are suitable for the characterization of exciton-exciton correlations in colloidal quantum dots and for the measurement of ultrafast exciton-exciton annihilation in molecular aggregates. The experiments performed in this thesis mark an important step towards the complete characterization of the nonlinear response of quantum systems. In view of this, the concept of fluorescence-detected multiple-quantum coherence multidimensional spectroscopy introduced here offers a unified, systematic approach. In virtue of the technical advantages such as the use of a single excitation beam and the absence of nonresonant contributions, the measurement protocols developed here can be directly transferred to other incoherent observables and to sample systems in other states of matter. Furthermore, the approaches presented here can be systematically extended to higher frequency dimensions and higher orders of nonlinearity. / Diese Arbeit beschreibt neuartige Konzepte zur Messung der statischen und dynamischen Eigenschaften der elektronischen Stuktur von Molekülen und Nanokristallen in der flüssigen Phase mittels kohärenter Fluoreszenz-detektierter Spektroskopie in zwei und drei Frequenzdimensionen. Diese Konzepte beruhen auf der systematischen Phasenvariation ("Phase Cycling") einer Sequenz mehrerer zeitverzögerter Femtosekunden-Anregepulse, um aus dem resultierenden phasenabhängigen Fluoreszenzsignal eine Vielzahl von neuartigen nichtlinearen Signalen zu dekodieren. Diese Signale stellen jegliche Permutationen von Korrelationen zwischen Null-, Ein-, Zwei- und Drei-Quantenkohärenzen dar. Hierzu wurden zwei neue Phase-Cycling Schemata entwickelt, welche gleichzeitig mehrere nichtlineare Signale der sechsten Ordnung auflösen und voneinander unterscheiden können, inklusive der Signale der vierten nichtlinearen Ordnung. Mit den in dieser Arbeit aufgenommenen Signalen der sechsten Ordnung können statische Eigenschaften hoch-angeregter elektronischer Zustände in Molekülen wie deren Energien, Übergangsdipolmomente, relative Verschiebung elektronischer Potentialflächen zueinander, sowie dynamische Eigenschaften in Bezug auf deren Relaxationskinetik ermittelt werden. Ferner wurde gezeigt, dass diese Signale zur Charakterisierung von Exziton-Exziton-Korrelationen in kolloidalen Quantenpunkten sowie zur Messung ultraschneller Exziton-Exziton-Annihilierung in molekularen Aggregaten geeignet sind. Die Experimente dieser Arbeit markieren einen wichtigen Schritt in Richtung der vollständigen Charakterisierung der nichtlinearen Antwort von Quantensystemen. Das hier eingeführte Konzept der Fluoreszenz-detektierten multidimensionalen Multiquantenkohärenz-Spektroskopie bietet hierfür einen vereinheitlichten, systematischen Ansatz. In Hinblick auf technische Vorteile wie der Verwendung eines einzigen Anregestrahls und der Abwesenheit von nichtresonanten Beiträgen lassen sich die hier entwickelten Messprotokolle direkt auf andere inkohärente Observablen und auf Probesysteme in anderen Aggregatszuständen übertragen. Ferner lassen sich die vorgestellten Ansätze systematisch auf höhere Frequenzdimensionen und nichtlineare Ordnungen erweitern.

Early methods of optical fiber communication systems haven't been much promising in terms of efficiency. The presence of various impairments in the fiber channel has forced researchers to uncover solutions in order to minimize those effects. With the advancement of technology, optical solutions were finally easier to implement in the system. To this day, optical compensation methods are still found to be as the best way to minimize fiber impairments. However, such technique does introduce enormous complexity to the system, in addition to a large cost. For that reason, the main focus had to shift to an alternative method. Electrical compensation techniques have provided the factor of simplicity to the optical communication system, not to mention that they are relatively cheaper than optical compensators. Furthermore, electrical schemes were found to handle fiber impairments in a relatively efficient manner. In this thesis, an optical fiber communication scheme using the direct-detection method is simulated. A frequency shifter in the optical domain will be used for the system to have a coherent like detection. At the receiver's side, a linear equalizer is realized to offset the linear effects caused by the fiber. To our knowledge, this will mark the first direct detection transmission system to pass the one thousand kilometre mark in fiber length. Furthermore, we simulate another optical fiber communication design using the coherent detection. A nonlinear compensator adapting the Volterra approach will be used to offset nonlinear impairments. Such performance will be compared to that of a linear compensator. Design trade-offs will be analyzed, and the nonlinear compensator is found to a improve performance when a dispersion compensation fiber (DCF) is introduced in the optical domain. / Thesis / Master of Applied Science (MASc)

Partially coherent interaction of the feedback light with the field in the laser cavity is affirmed with the fiber Bragg grating (FBG) stabilized 980-nm pump lasers, on the contrast of normally accepted totally incoherent state of operation in the “coherence collapse” regime. Coherence parameter y was defined in this paper to identify the fraction of feedback light working coherently. It is shown that y can be determined by fitting the measured power-difference versus pumping-rate curve to the simulation results. Experiments confirm that coherence parameter y decreases while the distance between the FBG and the laser facet increases, and vice versa. While, if the device is kept operating in the “coherence-collapse” regime, y would not change with the amount of feedback. This work will be help to improve the performance of the high power FBG stabilized 980-nm pump laser. / Thesis / Master of Applied Science (MASc)

This dissertation describes methods of mitigating radio frequency interference (RFI) in the frequency range 10-100 MHz, developing and evaluating coherent methods with which RFI is subtracted from the afflicted data, nominally resulting in no distortion of the underlying signals. This approach is of interest in weak signal applications such as radio astronomy, where the signal of interest may have interference-to-noise ratio much less than one, and so can be easily distorted by other methods. Environmental noise in this band is strong and non-white, so a realistic noise model is developed, with which we characterize the performance of signal parameter estimation, a key component of the proposed algorithms. Two classes of methods are considered: "generic" parameter estimation/subtraction (PE/S) and a modulation-specific form known as demodulation-remodulation ("demod--remod") PE/S. It is demonstrated for RFI in the form of narrowband FM and Broadcast FM that generic PE/S has the problem of severely distorting underlying signals of interest and demod-remod PE/S is less prone to this problem. Demod-remod PE/S is also applied and evaluated for RFI in the form of Digital TV signals. In both cases, we compare the performance of the demod-remod PE/S with that of a traditional adaptive canceling method employing a reference antenna, and propose a hybrid method to further improve performance. A new metric for "toxicity" is defined and employed to determine the degree to which RFI mitigation damages the underlying signal of interest. / Ph. D.

This dissertation focuses on the problem space of heterogeneous-ISA multiprocessors – an architectural design point that is being studied by the academic research community and increasingly available in commodity systems. Since such architectures usually lack globally coherent shared memory, software-based distributed shared memory (DSM) is often used to provide the illusion of such a memory. The DSM abstraction typically provides this illusion using a reader-replicate, writer-invalidate memory consistency protocol that operates at the granularity of memory pages and is usually implemented as a first-class operating system abstraction. This enables symmetric multiprocessing (SMP) programming frameworks, augmented with a heterogeneous-ISA compiler, to use CPU cores of different ISAs for parallel computations as if they are of the same ISA, improving programmability, especially for legacy SMP applications which therefore can run unmodified on such hardware. Past DSMs have been plagued by poor performance, in part due to the high latency and low bandwidth of interconnect network infrastructures. The dissertation revisits DSM in light of modern interconnects that reverse this performance trend. The dissertation presents Xfetch, a bulk page prefetching mechanism designed for the DEX DSM system. Xfetch exploits spatial locality, and aggressively and sequentially prefetches pages before potential read faults, improving DSM performance. Our experimental evaluations reveal that Xfetch achieves up to ≈142% speedup over the baseline DEX DSM that does not prefetch page data. SMP programming models often allow primitives that permit weaker memory consistency semantics, where synchronization updates can be delayed, permitting greater parallelism and thereby higher performance. Inspired by such primitives, the dissertation presents a DSM protocol called MWPF that trades-off memory consistency for higher performance in select SMP code regions, targeting heterogeneous-ISA multiprocessor systems. MWPF also overcomes performance bottlenecks of past DSM systems for heterogeneous-ISA multiprocessors such as due to significant number of invalidation messages, false page sharing, large number of read page faults, and large synchronization overheads by using efficient protocol primitives that delay and batch invalidation messages, aggressively prefetch data pages, and perform cross-domain synchronization with low overhead. Our experimental evaluations reveal that MWPF achieves, on average, 11% speedup over the baseline DSM implementation. The dissertation presents PuzzleHype, a distributed hypervisor that enables a single virtual machine (VM) to use fragmented resources in distributed virtualized settings such as CPU cores, memory, and devices of different physical hosts, and thereby decrease resource fragmentation and increase resource utilization. PuzzleHype leverages DSM implemented in host operating systems to present an unified and consistent view of a continuous pseudo-physical address space to guest operating systems. To transparently utilize CPU and I/O resources, PuzzleHype integrates multiple physical CPUs into a single VM by migrating threads, forwarding interrupts, and by delegating I/O. Our experimental evaluations reveal that PuzzleHype yields speedups in the range of 355%–173% over baseline over-provisioning scenarios which are otherwise necessary due to resource fragmentation. To enable a distributed hypervisor to adapt to resource and workload changes, the dissertation proposes the concept of CPU borrowing that allows a VM's virtual CPU (vCPU) to migrate to an available physical CPU (pCPU) and release it when it is no longer necessary, i.e., CPU returning. CPU borrowing can thus be used when a node is over-committed, and CPU returning can be used when the borrowed CPU resource is no longer necessary. To transparently migrate a vCPU at runtime without incurring a significant downtime, the dissertation presents a suite of techniques including leveraging thread migration, loading/restoring vCPU in KVM states, maintaining a global vCPU location table, and creating a DSM kernel thread for handling on-demand paging. Our experimental evaluations reveal that migrating vCPUs to resource-available nodes achieves a speedup of 1.4x over running the vCPUs on distributed nodes. When a VM spans multiple nodes, it is likelihood for failure increases. To mitigate this, the dissertation presents a distributed checkpoint/restart mechanism that allows a distributed VM to tolerate failures. A user interface is introduced for sending/receiving checkpoint/restart commands to a distributed VM. We implement the checkpoint/restart technique in the native KVM tool, and extend it to a distributed mode by converting Inter-Process Communication (IPC) into message passing between nodes, pausing/resuming distributed vCPU executions, and loading/restoring runtime states on the correct set of nodes. Our experimental evaluations indicate that the overhead of checkpointing a distributed VM is ≈10% or less than that of the native KVM tool with our checkpoint support. Restarting a distributed VM is faster than native KVM with our restart support because no additional page faults occur during restarting. The dissertation's final contribution is PopHype, a system software stack that allows simulation of cache-coherent, shared memory heterogeneous-ISA hardware. PopHype includes a Linux operating system that implements DSM as an OS abstraction for processes, i.e., allows multiple processes running on multiple (ISA-different) machines to share memory. With KVM-enabled, this OS becomes a hypervisor that allows multiple, process-based instances of an architecture emulator such as QEMU to execute in a shared address space, allowing multiple QEMU instances to emulate different ISAs in shared memory, i.e., emulate shared memory heterogeneous-ISA hardware. PopHype also includes a modified QEMU to use process-level DSM and an optimized guest OS kernel for improved performance. Our experimental studies confirm PopHype's effectiveness, and reveal that PopHype achieves an average speedup of 7.32x over a baseline that runs multiple QEMU instances in shared memory atop a single host OS. / Doctor of Philosophy / Computing devices are ubiquitous around us. Each of these devices is powered by specialized chips called processors. These processors take in instructions, process them, and produce output. Such processing is what enables us, humans, to send messages to our loved ones, take photographs, as well as carry out various business functions such as using spreadsheet software. The kinds of instructions these processors execute are classified into so-called Instruction Set Architectures or ISAs. Chip designers build processors adopting different ISAs for various applications ranging from computing on mobile phones to cloud computing data centers used by large technology companies. Within a data center, there are typically hundreds of thousands of computing devices that serve an organization's purpose to serve millions or even billions of users. Programming these computers individually to serve a collective goal is an arduous task requiring hundreds of software engineering experts. To simplify programming these computers on a large scale, this thesis envisions an abstraction where tens of devices appear as one computing unit to the programmer, allowing them to program multiple computers as if they are one. This allows for better resource utilization in the sense that the power of multiple computing devices can be pooled together without the need to acquire newer, larger, and more-expensive computers. Furthermore, such pooling allows the software to leverage multiple different ISAs on different computers instead of a single ISA on one computer. This thesis also envisions a way for software to run on multiple computers with potentially different ISAs without exposing the difficulty of managing them to the software engineers.

The transport of material in geophysical fluid flows is a problem with important implications for fields as diverse as: agriculture, aviation, human health, disaster response, and weather forecasting. Due to the unsteady nature of geophysical flows, predicting how material will be transported in these systems can often be challenging. Tools from dynamical systems theory can help to improve the prediction of material transport by revealing important transport structures. These transport structures reveal areas of the flow where fluid parcels, and thus material transported by those parcels, are likely to converge or diverge. Typically, these transport structures have been uncovered by the use of Lagrangian diagnostics. Unfortunately, calculating Lagrangian diagnostics can often be time consuming and computationally expensive. Recently new Eulerian diagnostics have been developed. These diagnostics are faster and less expensive to compute, while still revealing important transport structures in fluid flows. Because Eulerian diagnostics are so new, there is still much about them and their connection to Lagrangian diagnostics that is unknown. This dissertation will fill in some of this gap and provide a mathematical bridge between Lagrangian and Eulerian diagnostics. This dissertation is composed of three projects. These projects represent theoretical, numerical, and experimental advances in the understanding of Eulerian diagnostics and their relationship to Lagrangian diagnostics. The first project rigorously explores the deep mathematical relationship that exists between Eulerian and Lagrangian diagnostics. It proves that some of the new Eulerian diagnostics are the limit of Lagrangian diagnostics as integration time of the velocity field goes to zero. Using this discovery, a new Eulerian diagnostic, infinitesimal-time Lagrangian coherent structures is developed. The second project develops a methodology for estimating local Eulerian diagnostics from wind velocity data measured by a fixed-wing unmanned aircraft system (UAS) flying in circular arcs. Using a simulation environment, it is shown that the Eulerian diagnostic estimates from UAS measurements approximate the true local Eulerian diagnostics and can predict the passage of Lagrangian diagnostics. The third project applies Eulerian diagnostics to experimental data of atmospheric wind measurements. These are then compared to Eulerian diagnostics as calculated from a numerical weather simulation to look for indications of Lagrangian diagnostics. / Doctor of Philosophy / How particles are moved by fluid flows, such as the oceanic currents and the atmospheric winds, is a problem with important implications for fields as diverse as: agriculture, aviation, human health, disaster response, and weather forecasting. Because these fluid flows tend to change over time, predicting how particles will be moved by these flows can often be challenging. Fortunately, mathematical tools exist which can reveal important geometric features in these flows. These geometric features can help us to visualize regions where particles are likely to come together or spread apart, as they are moved by the flow. In the past, these geometric features have been uncovered by using methods which look at the trajectories of particles in the flow. These methods are referred to as Lagrangian, in honor of the Italian mathematician Joseph-Louis Lagrange. Unfortunately, calculating the trajectories of particles can be a time consuming and computationally expensive process. Recently, new methods have been developed which look at how the speed of the flow changes in space. These new methods are referred to as Eulerian, in honor of the Swiss mathematician Leonhard Euler. These new Eulerian methods are faster and less expensive to calculate, while still revealing important geometric features within the flow. Because these Eulerian methods are so new, there is still much that we do not know about them and their connection to the older Lagrangian methods. This dissertation will fill in some of this gap and provide a mathematical bridge between these two methodologies. This dissertation is composed of three projects. These projects represent theoretical, numerical, and experimental advances in the understanding of these new Eulerian methods and their relationship to the older Lagrangian methods. The first project explores the deep mathematical relationship that exists between Eulerian and Lagrangian diagnostic tools. It mathematically proves that some of the new Eulerian diagnostics are the limit of Lagrangian diagnostics as the trajectory’s integration times is decreased to zero. Taking advantage of this discovery, a new Eulerian diagnostic is developed, called infinitesimal-time Lagrangian coherent structures. The second project develops a technique for estimating local Eulerian diagnostics using wind speed measures from a single fixed-wing unmanned aircraft system (UAS) flying in a circular path. Using computer simulations, we show that the Eulerian diagnostics as calculated from UAS measurements provide a reasonable estimate of the true local Eulerian diagnostics. Furthermore, we show that these Eulerian diagnostics can be used to estimate the local Lagrangian diagnostics. The third project applies these Eulerian diagnostics to real-world wind speed measurements. These results are then compared to Eulerian diagnostics that were calculated from a computer simulation to look for indications of Lagrangian diagnostics.

Ocean surface transport plays a critical role in marine ecosystems, influencing the complex spatiotemporal patterns of both marine species and pollutants. The theory of Lagrangian coherent structures (LCSs) aims to identify fundamental patterns within time-dependent, nonlinear fluid flows. LCSs are material surfaces that act as dividing lines which fluid does not cross for a relevant period of time. LCS theory is still under active development, and there are multiple proposed ways to mathematically determine an LCS. Each proposed mathematical definition aims to capture the same physical properties, and some capture those properties more successfully and consistently than others. Here we examine two proposed definitions from the founder of the LCS field: finite time Lyapunov exponents (FTLEs) and geodesic detection. While geodesic detection was developed as an improvement on FTLEs, FTLEs remain the most popular method for using LCSs as an analytical tool. We apply both methods to a novel application. We analyze ocean surface current data in an area off the coast of central California slated for wind energy development, comparing their relative strengths and weaknesses both in theory and in practice.

Particle accelerators are machines to accelerate and store charged particle beams, such as electrons or protons, to the energy levels for various scientific applications. There are three basic types of particle accelerators: linear accelerators (linac), storage-ring (or circular) accelerators, and recirculating accelerators. The third type, also the most recent one, is designed to accelerate a particle beam in a short section of linac, circulate and then continue to accelerate it for energy boost or decelerate it for energy recovery. The modern recirculating machines possess the advantages to both accelerate and preserve the beam with high beam quality, as well as efficiently reuse the accelerating components. As modern accelerators push toward the high-brightness or high-intensity frontier by demanding particles in a highly charged bunch to concentrate in an ever-decreasing beam phase space, the interaction amongst particles via their self-generated electromagnetic fields can potentially lead to coherent instabilities of the beam and thus pose significant challenges to the machine design and operation. Microbunching instability (MBI) has been one of the most challenging issues for such high-brightness or high-intensity beam transport, as it would degrade lasing performance in the fourth-generation light sources, reduce cooling efficiency in electron cooling facilities, and eventually compromise the luminosity of colliding beams in lepton or lepton-hadron colliders. The dissertation work will focus on the MBI in modern recirculating electron accelerators. The research attempts to develop a comprehensive theoretical formulation of MBI with aspects including among various degrees of freedoms the beam itself, the beamline lattice optics, and incorporation of all relevant collective effects that the beam encounters, for example the coherent synchrotron radiation (CSR) and the longitudinal space charge (LSC) effects. This dissertation includes the following seven themes: 1) Development and generalization of MBI theory to arbitrary linear lattices and coupled beams with constant and varying energies; 2) Construction of CSR impedance models from steady state to transient state and from high to low energy regime; 3) Numerical implementation of the developed theory as a fast and numerical-noise-free Vlasov solver and benchmarking with massive particle tracking simulation; 4) Exploration of multistage cascaded amplification mechanism of CSR microbunching development; 5) Control of CSR-induced MBI in multi-bend transport or recirculation arcs; 6) Study of more aspects of microbunched structures in beam phase spaces; and 7) Study of MBI for magnetized beams and confirming the suppression of MBI for a recent cooler design for Jefferson Lab Electron Ion Collider project. / Ph. D. / Particle accelerators are machines to accelerate and store charged particle beams, such as electrons or protons, to the energy levels for various scientific applications. There are three basic types of particle accelerators: linear accelerators (linac), storage-ring (or circular) accelerators, and recirculating accelerators. The third type, also the most recent one, is designed to accelerate a particle beam in a short section of linac, circulate and then continue to accelerate it for energy boost or decelerate it for energy recovery. The modern recirculating machines possess the advantages to both accelerate and preserve the beam with high beam quality, as well as eciently reuse the accelerating components. As modern accelerators push toward the high-brightness or high-intensity frontier by demanding particles in a highly charged bunch to concentrate in an ever-decreasing beam phase space, the interaction amongst particles via their self-generated electromagnetic fields can potentially lead to coherent instabilities of the beam and thus pose significant challenges to the machine design and operation. Microbunching instability (MBI) has been one of the most challenging issues for such high-brightness or high-intensity beam transport, as it would degrade lasing performance in the fourth-generation light sources, reduce cooling eciency in electron cooling facilities, and eventually compromise the luminosity of colliding beams in lepton or lepton-hadron colliders. The dissertation work will focus on the MBI in modern recirculating electron accelerators. The research attempts to develop a comprehensive theoretical formulation of MBI with aspects including among various degrees of freedoms the beam itself, the beamline lattice optics, and incorporation of all relevant collective e↵ects that the beam encounters, for example the coherent synchrotron radiation (CSR) and the longitudinal space charge (LSC) e↵ects. This dissertation includes the following seven themes: 1) Development and generalization of MBI theory to arbitrary linear lattices and coupled beams with constant and varying energies; 2) Construction of CSR impedance models from steady state to transient state and from high to low energy regime; 3) Numerical implementation of the developed theory as a fast and numerical-noise-free Vlasov solver and benchmarking with massive particle tracking simulation; 4) Exploration of multistage cascaded amplification mechanism of CSR microbunching development; 5) Control of CSR-induced MBI in multi-bend transport or recirculation arcs; 6) Study of more aspects of microbunched structures in beam phase spaces; and 7) Study of MBI for magnetized beams and confirming the suppression of MBI for a recent cooler design for Je↵erson Lab Electron Ion Collider project.